Power graph of finite abelian groups

Let G he a group. The power graph Gamma(P)(G) of G is a graph with vertex set V(Gamma(P)(G)) = G and two distinct vertices x and y are adjacent, in Gamma P(G) if and only if either x(i) = y or y(j) = x, where 2 <= i,j <= n. In this paper, we obtain some fundamental characterizations of the power graph. Also, we characterize certain classes of power graphs of finite abelian groups.